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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.22 n.1 Antofagasta mayo 2003

http://dx.doi.org/10.4067/S0716-09172003000100001 

Proyecciones
Vol. 22, N o 1, pp. 1-13, May 2003.
Universidad Católica del Norte
Antofagasta - Chile

NONRESONANCE BELOW THE SECOND
EIGENVALUE FOR A NONLINEAR
ELLIPTIC PROBLEM

M. MOUSSAOUI and M. MOUSSAOUI
University Mohamed I, Oujda, Morocco

Abstract

We study the solvability of the problem

when the nonlinearity g is assumed to lie asymptotically between 0
and the second eigenvalue ¸ We show
that this problem is nonresonant.

 

Key words Eigenvalue, nonresonance, p-laplacian, variational approach.

References

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[9] M. MOUSSAOUI, A.R. EL AMROUSS Minimax principles for critical- point theory in application to quasilinear boundary-value problems E.J.D.E vol (2000) N 18 p 1-9.        [ Links ]

[10] M. MOUSSAOUI, M. MOUSSAOUI Nonlinear elliptic problems with resonance at the two first eigenvalue: A variational approach , preprint (2000).        [ Links ]

[11] M. MOUSSAOUI, M. MOUSSAOUI Nonresonance between non-consecutive eigenvalues of semilinear elliptic equations: Variational methods, preprint (2000).        [ Links ]

[12] JOAO. MARCOS. B. do Ó Solution to perturbed eigenvalue problems of the p-laplacian in RN *J. D. E. N 11, 1-15 (1997).        [ Links ]

[13] P. H. RABINOWITZ minimax methods in critical point theory with application to differential equations, CBMS, Regional conf. Ser. Math., vol 65 AMS, Providence Ri. (1986).        [ Links ]

[14] E. A. B. SILVA Linking theorems and applications to semilinear elliptic problems at resonance, Nonlinear Analysis TMA, 16, 455-477 (1991).        [ Links ]

Received : May 2002.

M. MOUSSAOUI
Department of Mathematics
Faculty of Sciences
University Mohamed I
P. O. BOX 524
60000 Oujda
Morocco
e-mail : moussaoui@sciences.univ-oujda.ac.ma

and

M. MOUSSAOUI
Department of Mathematics
Faculty of Sciences
University Mohamed I
P. O. BOX 524
60000 Oujda
Morocco
e-mail : mimoun moussaoui@hotmail.com

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